Your best bet as an entrepreneur is to find places that are owned by individuals rather than property management companies. Alot of families have rental properties like duplexes that have been family-owned for generations. Individuals with rental properties usual don't care about your situation as long as the rent is paid on time. You can also work out deals to avoid deposits. Individually owned places also like if you can pay cash, because then they can pocket the money and avoid declaring it as income on their taxes.
Another great option is month-to-month places, even weekly rental places. Those places are a good bet because not only do they not care about your income, but they also don't require deposits. Avoiding an upfront deposit gives you more cashflow to pay rent longer. For example, saving $800 on a deposit gives you $800 worth of rent money to keep a roof over your head an extra month. You also don't have to deal with the hassle of getting utilities in your name.
Here's how you deal with big apartment complex property management companies: just lie. Seriously. And give a friend's phone number as your "employer". Make up some fake paystubs in quickbooks. Big property management companies usually hire stupid people that sit in the office all day, do nothing, and collect a paycheck. They don't verify income, or any of the other things they request. Since they don't care, neither should you. Fuck 'em.
Another final comment about big apartment complexes: at a certain point, if you know you're going to move, just quit paying rent. Apartment complexes take a hands-off approach to evictions and actually file real eviction proceedings. As such, you can sit there and live rent free for an entire month or more while they file the legal paperwork against you. Save that rent money you're not paying and save it for when you do find another place.
About moving: It's a better deal to sell your stuff on craigslist instead of move it. You can recoup some cash from the sale plus people will pick-up the stuff for free. That not only makes you money, but it also saves you from having to pay for a moving truck or the hassle of moving the stuff. Better to sell your stuff, get some cash, and then get new stuff after you move. You can get decent stuff on craigslist after you move for cheap. Plus selling your stuff lets you re-assess how much of what you had that you really want to re-accumulate.